How does the previous analysis of trading intervals influence these stochastic results?
The analytical approach in [1]} does not include effects of trading at all but assumes random and uncorrelated noise to account for all frequency disturbances. One important finding of Fig. REF  is that the width of the distribution, i.e. the standard deviation or scale parameter of the probability distribution does not change dramatically when comparing trading and non-trading intervals. Only the heavy-tails are easily attributed to the trading.
Hence, the stochastic theory should be further developed to include non-Gaussian effects due to deterministic trading actions, instead of solely arising from random fluctuations.
However, the current form of the theory will still be able to predict the approximate width of a distribution if the noise amplitudes in the system are known.
